Lecturer: Julia Hörrmann
Thursday 8-10 am, Online via Zoom (Link: https://ethz.zoom.us/j/94532158621)
Course content:
The problem of reconstruction of an object from geometric information like X-ray data is a classical inverse problem on the overlap between applied mathematics, statistics, computer science and electrical engineering.
We focus on various aspects of the problem in the case of prior shape information on the reconstruction object. We will answer questions on uniqueness of the reconstruction and also cover statistical and algorithmic aspects.
Exercises:
We will discuss smaller exercises and open problems during the lectures. Matlab implementations of the discussed algorithms can be tried out at the website www.geometrictomography.com.
Prerequisites:
A sound mathematical background in geometry, analysis and probability is required though a repetition of relevant material will be included. The ability to understand and write mathematical proofs is mandatory.
Learning objective:
Introduction to geometric tomography and understanding of various theoretical aspects of reconstruction problems.
Exam:
There will be an oral exam.
Online office hour:
Friday, 9-10 am (zoom-link upon request via e-mail to julia.hoerrmann@inf.ethz.ch)
Lecture Notes:
LectureNotes_GeometricTomography
| Date | Topic | Lecture Notes | Solutions | Recording |
| 17.09.20 | Introduction | 2020-09-17_Script | 2020-09-17_Recording | |
| 24.09.20 | Background from convex geometry | 2020-09-24_Script | 2020-09-24_Solutions | 2020-09-24_Recording |
| 01.10.20 | Background from empirical process theory | 2020-10-01_Script | 2020-10-01_Recording | |
| 08.10.20 | Reconstruction from support function measurements | 2020-10-08_Script | 2020-10-08_Solutions | 2020-10-08_Recording |
| 15.10.20 | Reconstruction from support function measurements | 2020-10-15_Script | 2020-10-15_Solutions | 2020-10-15_Recording |
| 22.10.20 | Reconstruction from surface area measures | 2020-10-22_Script | 2020-10-22_Solutions | 2020-10-22_Recording |
| 29.10.20 | Reconstruction from surface area measures | 2020-10-29_Script | 2020-10-29_Recording | |
| 05.11.20 | Reconstruction from brightness function measurements | 2020-11-05_Script | 2020-11-05_Recording | |
| 12.11.20 | Reconstruction from brightness function measurements | 2020-11-12_Script | 2020-11-12_Recording | |
| 19.11.20 | Reconstruction from the covariogram | 2020-11-18_Script | 2020-11-18_Solutions | 2020-11-18_Recording |
| 26.11.20 | Reconstruction from the covariogram | 2020-11-26_Script | 2020-11-26_Recording | |
| 03.12.20 | Reconstruction from parallel X-rays | 2020-12-03_Script | 2020-12-03_Recording | |
| 10.12.20 | Reconstruction from parallel X-rays | 2020-12-10_Script | 2020-12-10_Recording | |
| 17.12.20 | Exam repetition | 2020-12-17_ExamRepetition |
References:
R. Gardner: Geometric Tomography
F. Natterer: The Mathematics of Computerized Tomography
A. Rieder: Keine Probleme mit inversen Problemen